1. Field of the Invention
This invention relates to apparatus and methods for reduction of B-integral accumulation in laser systems.
2. Description of the Related Art
Lasers which emit a pulse that rapidly varies between low and high intensity values are useful in many applications including laser drilling, laser cutting, linear acceleration, X-ray holography, and X-ray generation. However, special problems can arise in working with these lasers due to effects produced by their intensity variations.
One particular problem occurs due to a well-known process called self-phase modulation. Self-phase modulation occurs where a laser pulse having a sufficiently high, variable intensity enters an optical material such as a laser amplification medium. At high intensity levels, the index of refraction of an optical material varies non-linearly as the intensity of an entering laser pulse varies in time. This non-linear change in the index of refraction causes phase changes in the temporal distribution of the laser pulse as it enters the optical material.
These phase changes occur because the changes in the index of refraction of the laser amplification medium cause corresponding changes in the phase velocity of the entering pulse. In fact, any optical material, for example, glass or lenses, that the pulse passes through will cause some corresponding change in the phase velocity. Portions of the laser pulse entering the laser amplification medium at higher values of the index of refraction will be slowed to a greater extent than portions of the laser pulse entering the medium at lower values of the index of refraction. In the laser pulses in which self-phase modulation occurs, the existing time distribution of the laser pulse is modified by the variable intensity of the laser pulse passing through the variable index of refraction in the medium.
Once the entire pulse has entered the amplification medium, the differing portions of the pulse corresponding to differing intensities continue to move at different velocities within the amplification medium causing temporal and spatial distortions. For temporal distortions, the amount of phase accumulated in the pulse will be dependent upon the amount of time during which the pulse moves within the laser amplification medium. This amount of time will depend both upon the length of the medium and upon the number of round trips within the medium in which the laser pulse is reflected. After a number of trips through the medium, the phase changes in the pulse may be substantial and create significant temporal structures such as "wings" or a "pedestal."
These effects of self-phase modulation are often undesirable in laser applications. In typical laser pulses, the temporal structure created in the laser pulse will decrease the peak intensity delivered by the pulse, lengthen the pulse duration, and disrupt the energy output of the pulse. Thus, by reducing the temporal structure created in a pulse by self-phase modulation, one can provide shortened pulse duration, give better pulse-to-pulse energy stability, and allow for overall higher energy extraction from the generated laser pulse.
A quantity termed the "B-integral" measures the total non-linear phase accumulated in the peak intensity of the pulse. The B-integral thus identifies the extent of the maximum distortion of the pulse occurring due to self-phase modulation. Reduction of the accumulated B-integral is used herein to describe the reduction of the effects generated by self-phase modulation to negligible impact.
FIG. 1 shows the use of expansion and compression gratings with a pulsed laser 10 to shorten the pulse duration and reduce the effects of self-phase modulation. A pulse, which is generated by the pulse laser source 12, first passes through the expansion gratings 14, which create linear changes in the phase of the pulse, i.e., initially lengthening the pulse duration. In the laser amplification medium 16, gain narrowing causes the pulse to narrow in bandwidth as only certain frequencies in the pulse are amplified. Compression gratings 18 receiving the pulse exiting from the amplification medium 16 undo the effects of the expansion gratings 14 in the gain-narrowed pulse such that the pulse phase is linearly changed in a reverse fashion.
An additional prior-known method of compensation for self-phase modulation in a laser pulse entails altering the orientation of the compression gratings so that the linear phase change caused by the compression gratings does not only reverse the phase change produced by the expansion gratings, but corrects some of the phase shift produced by self-phase modulation. However, as self-phase modulation creates a non-linear phase in the pulse, the linear phase change of the compression gratings can only be used to compensate the effects of self-phase modulation on average. Compression gratings thus cannot be used to compensate for self-phase modulation exactly. Radially variant temporal structure will remain in the recompressed pulse.
The B-integral also measures the amount of "self-focusing" occurring in a high-intensity laser beam or pulse in which the intensity varies in space rather than in time. For spatial distortions, self-focusing is produced by interactions between the spatial variations in intensity of the laser beam or pulse with the non-linear index of refraction as it enters a laser amplification medium. For example, in a laser beam, the higher-intensity portions of the beam entering the medium at an oblique angle will be deflected more sharply toward the normal to the medium surface than will lower-intensity portions of the beam entering the medium at the same angle. This occurs because the sine of the angle of refraction of the pulse portion will vary inversely with the index of refraction of the medium for an equal index of refraction (at the edge of the medium) and incident angle. Therefore, the higher the intensity of the pulse portion and the higher the index of refraction of the medium, then the smaller the refraction angle will occur. Similarly, the lower the intensity of the pulse portion and the lower the index of refraction, then the larger the refraction angle will occur.
In any medium with a positive nonlinear index of refraction, a laser with a centrally peaked intensity profile is susceptible to self-focusing. The central portion of the laser accumulates a higher phase delay than the edges, in an analogous manner to a beam passing through a lens, and it begins to focus. If the effective focal length is short enough, the laser can focus to a small spot before exiting the medium, leading to catastrophic damage. This problem is exacerbated in a laser amplifier where the pulse energy continues to increase as it undergoes focusing.
Thus, reduction or cancellation of the B-integral is also desirable to prevent destructive self-focusing of the highest-intensity portions of a laser beam or pulse where the B-integral measures the spatial, rather than temporal, effects of spatial variations in the intensity.